Communication-Efficient and Error-Free Gradecast with Optimal Resilience

Gradecast is a variant of the Byzantine broadcast problem introduced by Feldman and Micali in 1988. In Gradecast, n processors would like to agree on a value sent from a leader, as well as a grade in {0, 1, 2}, such that the following three requirements are satisfied: 1) Every non-faulty processor outputs the leader’s initial value and grade 2 if the leader is non-faulty; 2) For any two non-faulty processors, if their decided grades are greater than zero, then they output the same value; and 3) For any two non-faulty processors, the difference of their decided grades is less than 2. In this work, we present a new Gradecast protocol with a total communication complexity of O(nℓ + n
²
log n) bits, given t < n/3, where ℓ is the message size and t is the maximum number of faulty processors tolerated in n consensus processors. The proposed protocol is an error-free and deterministic Gradecast protocol that does not rely on the authentication techniques such as signatures and secret sharing. The proposed protocol is also information-theoretic secure, i.e., it satisfies the above three requirements even if the computation power of the adversary is unbounded.